Calculus 3 : Vector Subtraction

Study concepts, example questions & explanations for Calculus 3

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Example Questions

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Example Question #1 : Vector Subtraction

Find the difference 

Possible Answers:

Correct answer:

Explanation:

The difference  of two vectors  and  is defined as

For the two vectors 

The difference is

Example Question #2 : Vector Subtraction

Given the vectors

find .

Possible Answers:

Correct answer:

Explanation:

Given the vectors

we can find the difference by subtracting component-wise

Example Question #3 : Vector Subtraction

Perform the following operation on the vectors specified below:

Where

Possible Answers:

Correct answer:

Explanation:

First, multiply out the vectors by their corresponding coefficients:

Now we simply subtract the two vectors:

Example Question #4 : Vector Subtraction

Subtract the vectors  and 

Possible Answers:

Correct answer:

Explanation:

Set up an expression to subtract the vectors.

Be sure to make note of the sign change when subtracting the vectors.

Simplify the vector.

The answer is:  

Example Question #5 : Vector Subtraction

Find the difference, , of the two vectors.

Possible Answers:

Correct answer:

Explanation:

To find the difference, , we distribute the minus sign and turn it into vector addition.

The sum of two vectors is defined as

The sum of two vectors 

is defined as 

As such, the difference is

Example Question #6 : Vector Subtraction

Compute the following: .

Possible Answers:

Correct answer:

Explanation:

The formula for subtracting vectors is . Plugging in the values we were given, we get 

Example Question #7 : Vector Subtraction

Solve:

Possible Answers:

Correct answer:

Explanation:

To subtract vectors, we simply subtract their respective components:

Note that our result is a vector still.

Example Question #8 : Vector Subtraction

Find the difference between  and .

Possible Answers:

Correct answer:

Explanation:

The formula for the difference of vectors is 

Using the vectors given, we get 

.

 

Example Question #9 : Vector Subtraction

Compute the following operation: .

Possible Answers:

Correct answer:

Explanation:

The formula for subtracting vectors a and b is 

.

Plugging in the values we were given, we get 

Example Question #10 : Vector Subtraction

Perform the following vector operation: 

Possible Answers:

Correct answer:

Explanation:

The formula for the difference of vectors  and  is . Using the vectors from the problem statement, we get 

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